# 3.2 Discounting - Solutions

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## 3.2 Discounting - Solutions

Pages:
9
School:
University of Texas at Austin
Course:
Fin 320f - Foundations of Finance
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Unformatted text preview:

Age: 25262728293031…59606162636465 End of period: 0123456…34353637383940 End of period: 012345678910 FIN 320F Foundations of Finance 3.2 Discounting – Solutions 1. Assume you are now 25 and you want to have a million dollars by the time you are 65. If you can earn 6% per year, compounded annually, how much must you invest today? PV = ? FV = \$1,000,000 FV = \$1,000,000 r = 6% per year n = 40 years m = 1 compounding per year N = 40 × 1 I% = 6 ÷ 1 PM T = 0 FV = 1000000 PV = AL PH A EN TE R = -97222 2. Your bank pays 2% interest, compounded daily, on all savings account balances. If you want to have \$10,000 in your account 10 years from now, how much must you deposit today? PV = ? FV = \$10,000 FV = \$10,000 r = 2% per year n = 10 years m = 365 compoundings per year (360 days is also okay—the answer is the same) N = 10 × 365 I% = 2 ÷ 365 SourceDocument.docx Page 1 of 9 ©HToprac 2015-2022 \$97,222 PV 0.0972 \$1,000,000 PV 1 40 1 .06 1 1 \$1,000,000 PV m n m r 1 1 FV PV                    \$8,187.35 PV 0.818735 \$10,000 PV 365 .02 1 1 \$10,000 PV m n m r 1 1 FV PV 365 10                    End of period: 0123456…24252627282930 End of period: 012345 FIN 320F Foundations of Finance 3.2 Discounting – Solutions PM T = 0 FV = 10000 PV = AL PH A EN TE R = -8187.35 3. As we learned in homework 3.1, college costs average \$23,410 for the 2014-2015 academic year. If the average annual increase in college costs has been 5% for the past three decades, what was average cost for one year of college 30 years ago? PV = ? FV = \$23,410 FV = \$23,410 r = 5% per year n = 30 years m = 1 compounding per year N = 30 × 1 I% = 5 ÷ 1 PM T = 0 FV = 23410 PV = AL PH A EN TE R = -5416.55 4. If you can finish a multi-year project on time and on budget, you will earn a \$5,000 bonus two years from today, plus another \$5,000 bonus 5 years from today. Assuming a discount rate of 5%, what is your potential bonus package worth today? PV = ? FV1 = \$5,000 FV2 = \$5,000 FV1 = \$5,000 FV2 = \$5,000 n1 = 2 years n2 = 5 years r = 5% per year r = 5% per year m = 1 m = 1 N = 2 × 1 SourceDocument.docx Page 2 of 9 ©HToprac 2015-2022 \$5,416.55 PV 87 0.23137744 \$23,410 PV 1 30 ...

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